A self-guided differential evolution with neighborhood search for permutation flow shop scheduling

Constructive heuristics and discrete harmony search are used to initialize.A guided agent based on the probabilistic model is proposed.Multiple mutation and crossover based on the guided agent are proposed.Neighborhood search based on the variable neighborhood search is designed.The convergence of the proposed algorithm is analyzed with Markov chain. The permutation flow shop scheduling problem (PFSSP) is one of the most widely studied production scheduling problems and a typical NP-hard combinatorial optimization problems as well. In this paper, a self-guided differential evolution with neighborhood search (NS-SGDE) is presented for the PFSSP with the objectives of minimizing the maximum completion time. Firstly, some constructive heuristics are incorporated into the discrete harmony search (DHS) algorithm to initialize the population. Secondly, a guided agent based on the probabilistic model is proposed to guide the DE-based exploration phase to generate the offspring. Thirdly, multiple mutation and crossover operations based on the guided agent are employed to explore more effective solutions. Fourthly, the neighborhood search based on the variable neighborhood search (VNS) is designed to further improve the search ability. Moreover, the convergence of NS-SGDE for PFSSP is analyzed according to the theory of Markov chain. Computational simulations and comparisons with some existing algorithms based on some widely used benchmark instances of the PFSSP are carried out, which demonstrate the effectiveness of the proposed NS-SGDE in solving the PFSSP.

[1]  Lin-Yu Tseng,et al.  A hybrid genetic local search algorithm for the permutation flowshop scheduling problem , 2009, Eur. J. Oper. Res..

[2]  Mehmet Fatih Tasgetiren,et al.  A particle swarm optimization algorithm for makespan and total flowtime minimization in the permutation flowshop sequencing problem , 2007, Eur. J. Oper. Res..

[3]  Swagatam Das,et al.  A Discrete Inter-Species Cuckoo Search for flowshop scheduling problems , 2015, Comput. Oper. Res..

[4]  Mehmet Fatih Tasgetiren,et al.  A discrete differential evolution algorithm for the permutation flowshop scheduling problem , 2008, Comput. Ind. Eng..

[5]  Mieczysław Wodecki,et al.  A very fast tabu search algorithm for the permutation flow shop problem with makespan criterion , 2004, Comput. Oper. Res..

[6]  Wojciech Bozejko,et al.  Solving the Flow Shop Problem by Parallel Simulated Annealing , 2001, PPAM.

[7]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .

[8]  Jigui Sun,et al.  An alternate two phases particle swarm optimization algorithm for flow shop scheduling problem , 2009, Expert Syst. Appl..

[9]  Minghao Yin,et al.  A discrete artificial bee colony algorithm with composite mutation strategies for permutation flow shop scheduling problem , 2012 .

[10]  Alexander Mendiburu,et al.  A Distance-Based Ranking Model Estimation of Distribution Algorithm for the Flowshop Scheduling Problem , 2014, IEEE Transactions on Evolutionary Computation.

[11]  Victor Fernandez-Viagas,et al.  On insertion tie-breaking rules in heuristics for the permutation flowshop scheduling problem , 2014, Comput. Oper. Res..

[12]  Qingfu Zhang,et al.  A Self-guided Genetic Algorithm for permutation flowshop scheduling problems , 2012, Comput. Oper. Res..

[13]  Bassem Jarboui,et al.  An estimation of distribution algorithm for minimizing the total flowtime in permutation flowshop scheduling problems , 2009, Comput. Oper. Res..

[14]  É. Taillard.  Some efficient heuristic methods for the flow shop sequencing problem , 1990 .

[15]  Xavier Tort-Martorell,et al.  Comparing three-step heuristics for the permutation flow shop problem , 2010, Comput. Oper. Res..

[16]  Inyong Ham,et al.  A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem , 1983 .

[17]  Éric D. Taillard,et al.  Benchmarks for basic scheduling problems , 1993 .

[18]  Ling Wang,et al.  A hybrid differential evolution method for permutation flow-shop scheduling , 2008 .

[19]  Yan-Feng Liu,et al.  A hybrid discrete artificial bee colony algorithm for permutation flowshop scheduling problem , 2013, Appl. Soft Comput..

[20]  Jose M. Framiñan,et al.  New hard benchmark for flowshop scheduling problems minimising makespan , 2015, Eur. J. Oper. Res..

[21]  Jacques Carlier,et al.  Ordonnancements à contraintes disjonctives , 1978 .

[22]  Xiangtao Li,et al.  An opposition-based differential evolution algorithm for permutation flow shop scheduling based on diversity measure , 2013, Adv. Eng. Softw..

[23]  S. Bansal.  Minimizing the Sum of Completion Times of n Jobs over m Machines in a Flowshop—A Branch and Bound Approach , 1977 .

[24]  Ying Liu,et al.  An effective differential evolution algorithm for permutation flow shop scheduling problem , 2014, Appl. Math. Comput..

[25]  Shih-Hsin Chen,et al.  Addressing the advantages of using ensemble probabilistic models in Estimation of Distribution Algorithms for scheduling problems , 2013 .

[26]  Dragan Vasiljevic,et al.  Handling ties in heuristics for the permutation flow shop scheduling problem , 2015 .

[27]  Ping Chen,et al.  Self-adaptive perturbation and multi-neighborhood search for iterated local search on the permutation flow shop problem , 2015, Comput. Ind. Eng..

[28]  Andreas C. Nearchou,et al.  Differential evolution for sequencing and scheduling optimization , 2006, J. Heuristics.

[29]  Yeu-Ruey Tzeng,et al.  A hybrid EDA with ACS for solving permutation flow shop scheduling , 2012 .

[30]  Pierre Hansen,et al.  Variable neighbourhood search: methods and applications , 2010, Ann. Oper. Res..

[31]  Liang Gao,et al.  A hybrid backtracking search algorithm for permutation flow-shop scheduling problem minimizing makespan and energy consumption , 2015, 2017 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM).

[32]  Rubén Ruiz,et al.  New high performing heuristics for minimizing makespan in permutation flowshops , 2009 .

[33]  Bo Liu,et al.  An Effective PSO-Based Memetic Algorithm for Flow Shop Scheduling , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[34]  Magdalene Marinaki,et al.  Particle swarm optimization with expanding neighborhood topology for the permutation flowshop scheduling problem , 2013, Soft Computing.

[35]  Pei-Chann Chang,et al.  Extended artificial chromosomes genetic algorithm for permutation flowshop scheduling problems , 2012, Comput. Ind. Eng..

[36]  Fuqing Zhao,et al.  A shuffled complex evolution algorithm with opposition-based learning for a permutation flow shop scheduling problem , 2015, Int. J. Comput. Integr. Manuf..

[37]  Godfrey C. Onwubolu,et al.  Scheduling flow shops using differential evolution algorithm , 2006, Eur. J. Oper. Res..

[38]  Xingsheng Gu,et al.  A novel particle swarm optimization algorithm for permutation flow-shop scheduling to minimize makespan ☆ , 2008 .

[39]  Rubén Ruiz,et al.  TWO NEW ROBUST GENETIC ALGORITHMS FOR THE FLOWSHOP SCHEDULING PROBLEM , 2006 .

[40]  Fardin Ahmadizar,et al.  A new ant colony algorithm for makespan minimization in permutation flow shops , 2012, Comput. Ind. Eng..

[41]  Xinyu Shao,et al.  An effective hybrid teaching-learning-based optimization algorithm for permutation flow shop scheduling problem , 2014, Adv. Eng. Softw..

[42]  Edward F. Stafford,et al.  On the Development of a Mixed-Integer Linear Programming Model for the Flowshop Sequencing Problem , 1988 .

[43]  Colin R. Reeves,et al.  A genetic algorithm for flowshop sequencing , 1995, Comput. Oper. Res..

[44]  Yeu-Ruey Tzeng,et al.  A new heuristic based on local best solution for permutation flow shop scheduling , 2015, Appl. Soft Comput..

[45]  Mehmet Sevkli,et al.  Differential Evolution Algorithm for Permutation Flowshop Sequencing Problem with Makespan Criterion , 2004 .

[46]  Minghao Yin,et al.  A hybrid cuckoo search via Lévy flights for the permutation flow shop scheduling problem , 2013 .

[47]  Chandrasekharan Rajendran,et al.  A No-Wait Flowshop Scheduling Heuristic to Minimize Makespan , 1994 .

[48]  Jing J. Liang,et al.  A Hybrid Discrete Harmony Search Algorithm for blocking flow shop Scheduling , 2010, 2010 IEEE Fifth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA).

[49]  Marius Iosifescu,et al.  Finite Markov Processes and Their Applications , 1981 .

[50]  Ahmed El-Bouri,et al.  An investigation of initial solutions on the performance of an iterated local search algorithm for the permutation flowshop , 2012, 2012 IEEE Congress on Evolutionary Computation.

[51]  Wei-Hsiu Huang,et al.  A block mining and re-combination enhanced genetic algorithm for the permutation flowshop scheduling problem , 2013 .

[52]  Quan-Ke Pan,et al.  An estimation of distribution algorithm for lot-streaming flow shop problems with setup times , 2012 .

[53]  Ching-Jong Liao,et al.  An ant colony system for permutation flow-shop sequencing , 2004, Comput. Oper. Res..

[54]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..